GLONASS ambiguity resolution in PPP is a challenge, mainly due to the presence of inter-frequency code biases. Variations associated with antenna type, receiver type and receiver firmware have been observed, making calibration a difficult undertaking. The are thus two common ways of fixing GLONASS ambiguities in PPP: 1) have a dense network of reference stations to accurately measure between-station slant ionospheric delays; and 2) use a network of stations with homogeneous equipment (i.e., same antenna, receiver and firmware). However, when using IGS stations to estimate satellite clock corrections, none of these two methods can be successfully applied on a global level. Fortunately, there is another solution.


For GPS, the ionosphere-free signal has a wavelength of 6 mm. As a result, we typically fix the widelane ambiguities first, which allows isolating the ambiguity on L1 with a wavelength of 10.7 cm. For GLONASS, the same principle can hardly be applied since widelane ambiguity fixing is contaminated by inter-frequency code biases. The good news is that the wavelength of the GLONASS ionosphere-free signal is much longer than for GPS:

where 9/32 times the L1 wavelength is approximately equal to 5 cm. While I thought for a long time that it would be too short for successfully ambiguity resolution in PPP, a quick investigation last summer revealed that it would indeed be feasible.


Since implementing a full network solution for the estimation of GLONASS integer satellite clocks required major changes in our existing software at NRCan, I opted for a simpler solution based on the PPP-AR strategy from JPL. It consists of saving the float ambiguity estimates and covariance of the network solution (or similarly, PPP solutions with fixed coordinates), and using those estimates to form double-differenced (DD) ambiguities at the user end. Fixing DD ambiguities then allows obtaining more precise position estimates at the user end.


I tested this concept using a network of stations in Canada with inter-station distances at times exceeding 1000 km, and I realized that I could fix more than 90% of the 5 cm ionosphere-free ambiguities for observation sessions of about 3 hours or more. The figure below shows the position repeatability in static mode with and without ambiguity resolution (AR) for GLONASS-only and GPS+GLONASS solutions. The impact of GLONASS AR is significant, often exceeding 20% in the longitudinal component, thereby confirming the validity of the proposed approach.


Repeatability of static position with and without GLONASS ambiguity resolution.

Repeatability of GLONASS-only and GPS+GLONASS static PPP solutions with and without ambiguity resolution (AR) for session lengths of: a) 1h b) 2h c) 3h d) 6 h. Percentages are included to characterize the improvement due to AR for each component


I am quite confident that this is the way to go for GLONASS AR with a global network of mixed receiver types. Since I am not actively working on this concept at the moment, I am hoping that someone will pick up this idea and test its impact on satellite orbit determination and even show the full end-to-end PPP solution with integer satellite clocks and/or UPD estimation.


For the details of the method, please download the full paper in the Journal of Geodesy or on ResearchGate.

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